Class 12

Math

3D Geometry

Three Dimensional Geometry

A line segment has length 63 and direction ratios are $3,−2,6.$ The components of the line vector are

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Find the equation of the plane passing through $(3,4,−1),$ which is parallel to the plane $r2i^−3j^ +5k^˙ +7=0.$

The lines which intersect the skew lines $y=mx,z=c;y=−mx,z=−c$ and the x-axis lie on the surface: (a.) $cz=mxy$ (b.) $xy=cmz$ (c.) $cy=mxz$ (d.) none of these

Find the vector equation of a line passing through $3i^−5j^ +7k^$ and perpendicular to theplane $3x−4y+5z=8.$

A plane passes through a fixed point (a, b, c). The locus of the foot of the perpendicular to it from the origin is the sphere

A line passes through the points $(6,−7,−1)and(2,−3,1)˙$ Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.

A line $OP$ through origin $O$ is inclined at $30_{0}and45_{0}→OXandOY,$ respectivley. Then find the angle at which it is inclined to $OZ˙$

The plane which passes through the point $(3,2,0)$ and the line $1x−3 =5y−6 =4z−4 $ is a. $x−y+z=1$ b. $x+y+z=5$ c. $x+2y−z=1$ d. $2x−y+z=5$

Find the equation of plane which is at a distance $14 4 $ from the origin and is normal to vector $2i^+j^ −3k^˙$